Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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THEOR. DE QUADRAT.
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<
s
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xml:space
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">Quoniam igitur F H, L K ſunt diametro B D parallelæ,
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ſuntque D F, D L æquales, oportet lineam H K, quæ duas
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F H, L K conjungit, à diametro B D bifariam ſecari; </
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<
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xml:space
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re eadem H K parallela erit baſi A C , & </
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<
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xml:space
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">E H K G
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xml:space
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con.</
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linea. </
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<
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xml:space
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">Itaque E C parallelogrammum eſt; </
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<
s
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xml:space
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">cujus oppoſita la-
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tera quum bifariam dividat diameter B D, erit in ea paral-
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lelogrammi centrum gravitatis . </
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>
<
s
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xml:space
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">Eâdem ratione
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xlink:label
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xml:space
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">9. lib. 1.
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Arch. de
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Æquipond.</
note
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gramma erunt H M, N O, P Q, & </
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>
<
s
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xml:space
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">ſingulorum centra gra-
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vitatis in linea B D. </
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<
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xml:space
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">Ergo & </
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<
s
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">figuræ ex omnibus dictis pa-
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rallelogrammis compoſitæ centrum gravitatis in eadem B D
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reperiri neceſſe eſt. </
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>
<
s
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xml:space
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">Iſta autem figura eadem eſt quæ portio-
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ni ordinatè fuerat circumſcripta. </
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<
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xml:space
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">Ergo figuræ portioni ordi-
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natè circumſcriptæ centrum gravitatis conſtat eſſe in B D por-
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tionis diametro. </
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<
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<
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IV.</
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<
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">circuli, centrum
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gravitatis eſt in portionis diametro.</
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</
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<
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<
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xml:space
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">Eſto portio hyperboles, vel ellipſis vel circuli dimidiâ pri-
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Fig. 4.</
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mum figurâ non major, A B C; </
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ſtendendum eſt, in B D reperiri portionis A B C gravitatis
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centrum.</
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</
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<
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<
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xml:space
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">Si enim fieri poteſt, ſit extra diametrum in E, & </
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<
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E H diametro B D parallela. </
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<
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xml:space
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">Dividendo itaque D C conti-
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nuè bifariam, relinquetur tandem linea minor quam D H;
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</
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<
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<
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">circumſcribatur portioni figura ordinatè ex
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parallelogrammis quorum baſes æquales ſint lineæ D F, & </
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<
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jungantur B A, B C. </
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<
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xml:space
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">Figuræ itaque portioni circumſcri-
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ptæ centrum gravitatis eſt in B D portionis diametro. </
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<
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xml:space
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">Sit hoc
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K, & </
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<
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">jungatur E K, producaturque, & </
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<
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">occurrat ei A L
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parallela B D. </
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<
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& </
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<
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">exceſſus quo figura circumſcripta portionem ſuperat, mi-
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nor parallelogrammo B F, uti ſupra demonſtratum fuit ;</
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>
<
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note
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erit major ratio portionis A B C ad dictum exceſſum, quàm
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trianguli A B C ad B F parallelogrammum, id eſt </
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